Difficulty understanding Keras LSTM fitting data
Yes, intuition says that RNNs like LSTM or GRU will work better in your case, because predicted values might depend on input patterns corresponding to much earlier time intervals.
There is no reason to create samples shifted by a single measurement because many of the samples will contain pretty much the same information for your model. A viable approach is to shift by sample size. Keeping some overlap between samples is feasible as well. 


Keep in mind that as a general rule for processing audio data, it makes sense to convert raw audio data into vectors representing audio spectrum before feeding it into LSTM RNN (see this video for e.g. https://www.coursera.org/learn/nlp-sequence-models/lecture/sjiUm/speech-recognition).

Batch size is different from sample or window size in your case.